From what I can remember from the beginning of the Clone Wars animated series and the films, every time we see Grievous he get outmanoeuvred by some Jedi and almost gets captured.
After all his failure how can he still be the best general the Separatist army have and not be replaced already? The Separatists have lots of population from which to get a better general.
Yes, General Grievous did display significant tactical abilities multiple times.
General Grievous was a brilliant Separatist military strategist and a feared Jedi hunter -StarWars.com
Before his cyborgization, Grievous was a warlord on his home-planet, which would have required tactical skill of smaller scale.
Rising Malevolence demonstrated his mastery of the surprise attack.
Narrator: The Clone starfleet is under siege! Dozens of Republic warships have been destroyed in merciless surprise attacks that leaves no survivors.
In Grievous Intrigue, he correctly predicted the behavior of both Obi-Wan Kenobi and Anakin Skywalker based off previous encounters in order to lay a trap for them.
TV-94: The General's description of your tactics have been 100% accurate today. Very impressive, even by my standards.
In Heroes on Both Sides Grievous orchestrated and successfully acted out a terrorist attack on Coruscant, resulting in the obstruction of peace and the continuation of the Clone Wars. This showed political tact, in addition to his regular war-waging skills.
In Massacre, Grievous successfully commanded the near-genocide on the Nightsisters.
His forces later went on to successfully defeat the Shadow Collective, which was no mere feat.
In Revenge of the Sith he was able to successfully organize the capture of Supreme Chancellor Palpatine, though we don't know how hard that actually was, given his relation with Sidious.
You have to remember that he was being manipulated from the beginning by Darth Sidious. His purpose wasn't to win the Clone Wars, it was to escalate them to the point where nearly every Jedi had to become involved. His purpose required some tactics, but he had a disposable army of droids at his command, and could afford to make mistakes others couldn't. He could afford to commit war crimes, because the real manipulator didn't care about the separatists image, resources, or ability to sustain itself after the war.
